limx->0 (xcot(x))1/x² I tried L hospital rule but it is a very different form , I also tried taking log but it didn't work.

limx->0 (xcot(x))1/x² I tried L hospital rule but it is a very different form , I also tried taking log but it didn't work.

Show that f(x) is continuous at x=a if and only if lim(h→0) f(a+h) = f(a). How?

Limx→1 (√x2+6x)-(√7) / (x-1)

limθ→0 (5cos2θ-5)/(4θ)

Limx→-2 ((2/3)+(4/x-4))/(x+2)

I mostly have the question of what each one is asking me to draw. For example I have these three conditions f(-1) = DNE limx→-1 f(x) = -2 limx→4 f(x)...

limx→0 xsinx

Well I know that the limit L is equal to eight. I know I get 8 by plugging in the 2 into 3x+2, but then it asks me the following: (a) Find δ > 0 such that |f(x) − L| < 0.01...

I have tried using math calculators like symbolab and wolframalpha but they all cannot compute when I put the limit from the positive end. I know the answer is either 0 or DNE. But I cannot work it...

n are natural numbers, and a is a real positive number. I can find N in terms of a but this question is from a epsilon-delta limit chapter, so I have no idea how to find it whilst relating it...

lim sin2x x->0 x

Don’t the both of them mean the same? i.e from 2 to infinity? There was this one mcq which had both of these options. So how do yoy differentiate between the two?

O, 5, 6 or 6,

if f(n+1)=1/2( f(n)+(9/f(n)) ) , n€N and f(n)>0 for all n€N then find lim n-infinity f(n) .

lim x-o ((sinx/x))^(1/x) = 1

lt n-infinity ((q^n) + (p^n))^(1/n)

lt x-o( (2x-log(1+2x))/x^2 )

I am struggling as i know the sequence but got no idea how to describe it mathematically!

I want an answer with Q in it if it depends on it, which I'm quite sure of.

lim x->1 (tan(πx/4)-1)/(sin(πx)) Answer is -1/2 I tried to apply multiply up and down by the numerator conjugate and then don't know how to proceed. Is this even necessary? or is there...

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